AGRICULTURAL
ECONOMICS
ELSEVIER
Agricultural Economics 27 (2002) 15-22
www.elsevier.com/locate/agecon
Downward sloping demand for environmental amenities and
international compensation: elephant conservation
and strategic culling
Erwin Bulte a,*, G. Cornelis van Kooten b
b
a Department of Economics, Tilburg University, P. 0. Box 90153, 5000 LE Tilburg, The Netherlands
Department of Agricultural Economics, University of British Columbia, Rm. 303, Henry Angus Building,
2054 Main Mall, Vancouver, BC, V6T JZ2 Canada
Received 1 December 1997; received in revised form 30 August 2000; accepted 1 January 2001
Abstract
Conventional wisdom holds that monetary compensation for positive trans boundary externalities will promote conservation
of resource amenities. We demonstrate that, in the case of elephant conservation, international transfers may also result in
strategic behavior by host countries, with adverse implications for global welfare and in situ stocks. © 2002 Elsevier Science
B.V. All rights reserved.
Keywords: Declining marginal preservation value; Strategic choice; International compensatory transfers; Elephant conservation
1. Introduction
The economic rationale for preserving environmental amenities and conserving natural resources is often
partially, though certainly not always exclusively,
based on non-use values. Conservation of wildlife
resources in developing countries is likely to involve
positive externalities, with non-use values accruing to
people in different countries, usually developed ones.
Transboundary non-use values (e.g., for preservation
of wildlife) for which the "host" country is not fully
compensated may lead to sub-optimal provision from
a global perspective, as pointed out by Barbier and
Swanson (1990) in the context of elephant management. It is often argued that compensating for positive
externalities is in the interest of nature conservation,
* Corresponding author. Fax: +31-13-466-2072.
E-mail addresses: [email protected] (E. Bulte),
[email protected] (G. Comelis van Kooten).
and should be pursued through international conventions and agreements. It is well documented that
the mismatched timing between transfers and conservation investments by the range states may result
in reneging and agreements that are not renegotiating proof. In this paper, we focus on another, less
well-known effect of providing transfers. We demonstrate that the alleged positive effects of international
transfers may never materialize because transfers
may provoke strategic behavior by the host country,
resulting in loss of welfare for the international community and excessive depletion of the resource. This
is demonstrated for the case of African elephants.
2. Downward sloping demand
for environmental amenities
Empirical work on non-use values has largely
ignored declining marginal preservation value. Loomis
0169-5150/02/$ -see front matter © 2002 Elsevier Science B.V. All rights reserved.
PH: S0169-5150(01)00053-6
16
E. Bulte, G. Camelis van Kooten! Agricultural Economics 27 (2002) 15-22
and White (1996) and Bulte and van Kooten (1999a)
have recently summarized empirical contingent valuation work, concluding that the bulk of research is
directed at willingness to pay (WTP) to avoid species
extinction. For example, the overview by Bulte and
van Kooten indicates that, out of a sample of 30 recent CVM studies, not less than 24 were aimed at
measuring WTP for a 100% change in population.
(While some studies aimed to establish estimates
for the WTP to double the current population, the
majority focused on the possibility of extinction.)
However, the limited empirical work that has tried
to measure downward sloping demand for environmental amenities and resources indicates that the
demand for "nature" is indeed subject to diminishing returns (Tanguay et al., 1993; Loomis and
Larson, 1994; Montgomery et al., 1994; Brown et al.,
1994).
The implications of downward sloping demand
for environmental amenities (or, declining marginal
preservation value) on optimal stocks has been analyzed by Bulte and van Kooten (1999a) for the
case of minke whales in the northeast Atlantic.
Not surprisingly, they conclude that optimal whale
stocks are highly sensitive to assumptions concerning marginal WTP (MWTP) for preservation of
whales. Both strict conservation and extinction can
be justified for the same total preservation value
(the area under the MWTP or demand function),
just by varying the "slope" of the (linear) demand
function. Their results also confirm the conventional
wisdom that, irrespective of the specification of
marginal preservation value, internalizing (positive)
external effects is in the interest of nature conservation.
An alternative reason for providing international
transfers, especially relevant for the case of elephant conservation analyzed below, is the following.
Anderson (1992) argues that people in developed
countries were willing to adopt the 1989 trade ban in
ivory primarily because they did not have to compensate African countries for the economic losses they
would incur (see also Milliken, 2000). Upon comparing optimal stocks of elephants in Zambia with and
without a trade ban on ivory, Bulte and van Kooten
(1999b) found that, for most discount rates, elephant
stocks are greater with the trade ban than without it.
However, protecting elephants cost some $75-700 per
additional elephant, again depending on the discount
rate. For the higher rates of interest characteristic of
developing countries, the trade ban can protect elephants at the (relatively modest) cost of about $120
per elephant. As Anderson (1992) argues, preferences
for elephant conservation may be especially strong
in developed countries, so it seems "fair" that they
should compensate Zambia.
The standard result that internalizing positive
externalities promotes conservation of nature depends
critically on the (unrealistic) assumption that an international governing body exists to ensure a cooperative
solution, or that national governments can somehow be
tempted to agree to the global optimum (e.g., Sandler,
1997). We do not review cooperative solutions, but,
rather, discuss the use of compensation payments for
conservation of wildlife. Specifically, we study the
role of international transfers to African range states
that are an increasing function of the protected elephant population, as advocated by, e.g., Schulz and
Skonhoft (1996) and Skonhoft and Solstad (19981
The latter authors, studying pastoralist decision mak·
ing when wildlife and livestock compete for forage.
write " ... an international payment for conservatior,
linked to the stock of wildlife will give [... ] inceu
tives to increase the wildlife stock and therefore brin.
the market solution more in accordance to what is so
cially optimal" (Skonhoft and Solstad, 1998, p. 256)
However, we show that international transfers tht,
aim to internalize external effects of conservation rna;.
not contribute to wildlife conservation. Indeed, the
opposite effect may occur. To show this, we extend ru1
existing model of elephant management by Bulte and
van Kooten (1996) to include international paymentr·
by developed countries to protect elephants, demonstrating that selfish range states can sometimes improve their welfare by choosing an excessive depletion
strategy.
3. Wildlife management and compensation
for elephant protection
Assume that the international community derives
utility U(x) from elephant conservation, but chooses
not to compensate the host country for this externality. To focus the model and discussion we
will ignore the problems associated with poaching
E. Bulte, G. Cornel is van Kooten/ Agricultural Economics 27 (2002) 15-22
ivory (but see Millner-Gulland and Leader-Williams,
1992; Leader-Williams et al., 1990; Bulte and van
Kooten, 1999b). The model also simplifies reality by
overlooking the possibility to store ivory. While this
assumption does not affect the steady state results
reported below, it does affect the transitional paths
towards equilibria (see Kremer and Morcom, 2000).
The management problem for African countries can
then be represented by
Max
fooo [R(x) + py- D(x)]e-rt dt
(1)
subject to
dx
dt
(2)
=.X= G(x)- y.
In the objective function (1), x is the stock of elephants, R(x) the recreation benefits, y the harvest level
(i.e., the first two arguments in the objective function
represent use values), p the price of ivory on a per
elephant basis, D(x) the agricultural benefits foregone
as a result of elephant conservation, and r the social
discount rate. Non-use values are assumed to exist,
but accrue to people in different countries who choose
to free ride. Since no compensation for these non-use
values is provided they are ignored by range states.
In the equation of motion (2), G(x) is the growth
function.
The associated current value Hamiltonian is H =
R(x)+py- D(x)+A.[G(x)-y ], where A. is the co-state
multiplier measuring the shadow price of the stock at
the margin. Assuming an interior solution and that a
steady state exists, the maximum principle yields the
following well-known equations to describe the steady
state (see Clark, 1990)
r
=G
G(x*)
, *
(x )
=
y*
+
R' (x*) - D' (x*)
p
,
(3)
(4)
where * indicates an optimum solution in the case
of no compensation for the non-use benefits that accrue to foreigners. From (3), the optimal stock of elephants results when the social discount rate equals the
growth rate plus the marginal rate of substitution between leaving an elephant in situ and harvesting it today. Given the standard assumption that G" (x) < 0,
it follows from (4) that increasing marginal recreation
17
benefits, R'(x), raises the optimal stock x* unambiguously, with an increase in D' (x) having the opposite
effect. From (4) it also follows that, in the steady state,
harvest should equal net growth. This model is readily
solved when G(x), R(x) and D(x) are specified, which
is done in the next section.
Extending the model by Bulte and van Kooten
(1996), assume that the international community
ceases to free ride, so that range states no longer
bear the burden of protecting elephants alone. Define
¢ (x, z) = U (x) + V (z) as the additively separable utility function of the international community,
where z is consumption of other goods. Assume that
marginal preservation value is declining in stock size
(i.e., U' (x) > 0, U" (x) < 0), and that donor countries pay compensation based on the marginal value
of elephants preserved, and not according to the cost
of protecting them (as noted above). It is easy to
show that this form of compensation unambiguously
increases optimal stock size. The reason is that there
would now be an extra term, U' (x), in the numerator
of the stock term in Eq. (3), which, due to the concavity of the growth function, implies that optimal
stocks should go up (since U' (x) > 0).
A different solution results if African countries
are able to collude in order to maximize the overall
transfer payments they receive as compensation for
transboundary non-use values. With marginal preservation value declining in stock size, the compensation
received per elephant is subject to the discretionary
choices of range states with respect to harvesting.
Thus, African countries could potentially (and, if possible, should) act as a monopolist, raising the price
by restricting supply. (The limitations of monopoly
behavior are discussed later in the paper.) The difference with conventional models is that the monopolist
does not receive a price for a flow, but rather for the
stock it preserves.
In this case, the objective function for the African
range states becomes
Max
{XJ [R(x) +
py
+ T(x)x-
D(x)]e-rt dt
(5)
where T represents the transfer received per elephant,
with T (x) = U' (x). Consistent with economic intuition we assume U" (x) = T' (x) < 0. Maximizing (5)
subject to (2) gives the associated current value Hamiltonian, H = R(x)+py+T(x)x-D(x)+A.[G(x)-y].
18
E. Bulte, G. Cornelis van Kooten/Agricultural Economics 27 (2002) 15-22
Again, assuming a steady state, this problem is readily
solved for the following steady state equations:
Table 1
The savanna elephant of east and southern Africa, population
estimates•
r = G'(x**)
Country/region
R' (x**)
+ T' (x**)x** + T (x**) -
D' (x**)
+------------------------------p
(6)
G(x**) = y**
(7)
where ** indicates an optimum solution for this case.
Since G(x) is concave, the optimal stock increases
when the stock term on the RHS of (6) goes up. Obviously, T(x**) > 0, and thus this term contributes to
conservation. This can be termed the conservation motive of international transfers. On the other hand, by assumption, T' (x**) < 0 (hence also T' (x**)x** < 0).
This is what we call the depletion motive. Hence, the
stock term of (6) is greater than the stock term of
Eq. (3) when T (x**) > T' (x**)x**, and smaller when
the reverse is true. In that case, international compensation for a positive externality reduces African elephant stocks. We now solve both models for various
assumptions about preservation value at the margin.
4. Empirical results
Precise data on non-use values are lacking, so
it is not possible to rigorously assess optimal elephant stocks. Nevertheless, it is certainly possible to
"ballpark" the analysis and to demonstrate the possible effect of strategic culling outlined above in a
numerical analysis. The African elephant (Loxodonta
africana) consists of two sub-species that occupy
the forests of west and central Africa (Loxodonta
africana africana) and the open range (savannah) of
east and southern Africa (Loxodonta africana cyclotis). Due to their genetic differences, both warrant
independent conservation status (Said et al., 1995).
The savannah elephant is better known than the forest
elephant, probably because they are easier to view and
a larger sub-species. The west African elephant tends
to be a bit smaller and lives in thick bush. This not
only makes it difficult to view, but also to inventory.
Thus, Said et al. (1995) estimate that there exist about
82 000 elephants in Gabon, but this is a probable and
possible estimate (their terminology), not a definitive
Kenya
Tanzania
East Africa
Zimbabwe
Botswana
Zambia
Namibia
South Africa
Southern Africa
Estimated population
25000
98000
127000
81500
80000
32500
11500
10000
218000
a Includes "definite", "probable" and "possible" categories of
estimates, but not "speculative". Source: adapted from Said et al.
(1995, pp. 17-19).
estimate. In comparison, Said et al. are definite that
there are approximately 13 000 elephants in Kenya.
Hence, we focus on the savannah elephant of which
there are some 345 000 (see Table 1).
We employ the following estimates of D(x) and R(x·
from Bulte and van Kooten (1996, 1999b): R(x) =
.B ln(x), where .B = 42.27 million; and D(x) = 165x
Millner-Gulland and Leader-Williams ( 1992) indicate
that the intrinsic growth rate of elephants is 0.067. As·
suming a carrying capacity for the savanna elephants
that is double extant numbers and a logistics growth
function, G(x) = 0.067x(l - x/690000). Our research indicates that raw ivory prices have fallen from
about $300/k.g in the early 1980s to perhaps as low
as $25/k.g in the mid 1990s. While the ivory trade
ban may have contributed to the price decline, it also
forced more ivory into the black market, making it difficult to determine prices. Average tusk size has also
decreased over the past several decades from about 6
to 5 kg. By assuming a price of $100/k.g and average
tusk size of 5 kg, the price of an elephant is $1000.
As mentioned above, information about the non-use
values of elephant management is lacking. Indeed,
there are only a few studies aimed at estimating
non-use values for large mammals, but these have
focused mostly on whales. We heroically assume that
WTP to protect gray whales is roughly comparable
to non-use values for elephants. Given that WTP
for whales is about $20 per household (Loomis and
Larson, 1994), but that the forest and savanna elephants are near perfect substitutes (as is the Asian
E. Bulte, G. Corne lis van Kooten/ Agricultural Economics 27 (2002) 15-22
elephant, Elephas maximus), we assume household
WTP is $10 annually. Given that there are about 200
million households in the richer, developed countries,
this implies that the total annual WTP to preserve
savanna elephants is $2 billion. The accuracy of these
assumptions will affect our numerical results (in an
unknown direction), but we are less interested in the
absolute magnitude of the results than in the qualitative ones.
We assume a linear, downward sloping MWTP
curve, U 1 (x) = a - bx. Let A = $2 billion be the area
under U'(x). Then U'(x) =a- (a 2 j2A)x. We analyze the impact of various assumptions about MWTP
value by varying a, or the non-use value of the first
elephant.
First we solve the no-compensation case and then
the case where range states do not behave strategically.
The results of the no-compensation case do not depend
on the specification of U' (x) = T (x) and are reported
in the first row of Table 2 for various discount rates between 0% (no discounting) and 18% (a high rate typical of many developing countries). In the real-world
case of no compensation, optimal elephant stocks are
well below those currently in existence (345 000 elephants) at all discount rates. Optimal stocks are highly
sensitive to the discount rate, as one might expect, with
stocks only 40% of current stocks for the discount rate
of 18%. If left to their own devices (e.g., without a
trade ban or monetary compensation), it is optimal for
Table 2
Optimum elephant populations in Africa for various assumptions
about compensation, discount rates and marginal values of the first
elephant
Item
Discount rate
0%
6%
12%
18%
266820
212190
168687
138626
Compensation with no strategic behavior
a=$5000
690000
690000
a=$10000
397250
394894
a= $15 000
278084
265768
a=$25000
266820
212190
690000
392538
264716
168687
690000
390182
263664
159716
Compensation with strategic culling
a=$5000
394599
389973
a=$10000
201454
200283
a=$15000
135012
134490
a=$25000
81300
81112
385349
199112
133969
80924
380727
197942
133447
80736
No compensation
19
range states to reduce their elephant herds below what
they are now and below globally-optimal numbers (see
below). This might explain why some range states (especially in southern Africa) already cull their elephant
herds and have sought ways around the ivory trade ban
or its modification (see Bulte and van Kooten, 1999b).
The case of compensation with no strategic behavior is also reported in Table 2, but for various assumptions about T(x), i.e., about the value of parameter a.
It is obvious that, relative to the "no-compensation"
case, compensation with no strategic behavior results
in higher optimal stocks, although stocks decline as
the marginal value of preserving the first elephant increases. Note that, even if compensation for non-use
values is provided, there are many combinations of parameters yielding efficient stock levels that are smaller
than cunent elephant stocks.
For those in the conservation movement, this is a
disturbing result. At the margin, culling elephants and
reducing the existing stock can enhance welfare. The
reason is that, by culling elephants, those in the range
states obtain benefits from sale of ivory and reduced
damages to crops (and lives) that exceeds the any potential loss in tourism benefits and non-use values in
developed countries. Finally, note that for sufficiently
steep demand curves, WTP at the margin is zero for
the efficient stock levels in the steady state of the compensation case, hence no compensation is forthcoming
(compare the case of a = 25 000 for discount rates
lower than 12% with the no-compensation case).
WTP at the margin is lower as the steady-state stock
increases. This explains why providing a transfer is
"more effective" in promoting elephant conservation
when discount rates in range states are high (and their
preferred domestic stocks are relatively small). Compare the no-compensation case and the case where a =
10 000. For r = 0%, the transfer increases the extant
elephant population by 119166 animals, whereas the
increase for r = 18% is not less than 251556 elephants.
The main range states for the savanna elephant are
indicated in Table 1. Suppose these countries are able
to form a cartel in order to maximize compensation
payments from developed countries. They do this by
pursuing a joint management strategy that involves
stricter enforcement to increase stocks or culling to
reduce them. Solving the steady state described by
Eqs. (6) and (7) yields the results reported in last four
20
E. Butte, G. Corne lis van Kooten/Agricultural Economics 27 (2002) 15-22
rows of Table 2. It is clear that strategic responses of
African host countries to international compensation
schemes for non-use values lower the elephant stocks
that would be preserved in the absence of such strategic behavior. While compensation under these circumstances could lead to higher elephant stocks than in
the absence of such payments, if the WTP to protect
the first elephant exceeds about $8000, the depletion
motive of transfers outweighs the conservation motive
and greater elephant protection occurs when there is
no compensation.
When international demand for non-use values of
elephant conservation is steeply downward sloping
(i.e., when a is relatively large), the subsidy that
range states receive per elephant is highly sensitive
to the extant population and the depletion motive
outweighs the conservation motive. Then, stocks are
lower when international compensation for non-use
values are provided; indeed, they may even be below
what range states would be willing to protect without
compensation. It is not possible, a priori, to determine
if compensation will lead to higher or lower elephant
populations than in its absence. Knowing what developed countries are willing to pay to preserve elephants
is inadequate; it is also necessary to know the shape
of the compensation function or the MWTP function.
To what extent are range states able to behave strategically? It depends to some extent on the degree of
substitutability between forest and savanna elephants.
Further, given that the range states identified in Table 1
are divided on their approach to the ivory trade ban,
it may well be unrealistic to expect them to cooperate by forming a cartel to take advantage of compensation payments. Anything that we might say in this
regard is mere speculation, because behavior might
change if compensation was actually forthcoming. It
might also change if, for whatever reason, wildlife
ministries in various countries were to act in concert
(e.g., through creation of a supranational elephant conservation agency). Even in the absence of a cartel,
range states might be able to behave as oligopolists. In
this case, the outcomes will fall somewhere between
the strategic and non-strategic extremes reported in
Table 2 (see Varian, 1992, p. 290). Another possible
constellation is the model where a dominant cartel operates with a competitive fringe of price taking range
states (see Hartwick and Olewiler, 1998, pp. 299-300).
It may be that the utility those in developed countries receive from elephant conservation is independent of elephant numbers, as long as their survival is
guaranteed (e.g., herd size remains above minimum
viable population). Perhaps WTP for elephant conservation simply represents a "warm glow" that people
get from contributing to a good cause. If this is the
case the ability of range states to behave strategically
is very limited, but compensation might then be regarded as a lump sum payment, in which case the behavior of range states would not be different from the
no-compensation case. However, given the very existence of the ivory trade ban when elephants are not in
any real danger of disappearing at this time (i.e., there
remain sufficient numbers to guarantee their survival),
we expect that WTP is indeed a function of in situ
stocks.
Finally, Table 3 summarizes some results from a
sensitivity analysis. We have considered four alternative scenarios, assuming a discount rate of 12%
throughout. First, we compute optimal elephant stocks
when African range states are not allowed to trade
ivory, consistent with the current CITES trade ban.
Table 3
Sensitivity analysisa
Optimal stocks
No trade
Increase total WTP
(A= $4 x 109 )
Increase recreation benefits
(R(x) = 84.6 x 106 ln(x))
Increase agricultural
damage (D(x) = 330x)
No compensation
256364
168 687
305131
104868
690000
392541
264 717
160097
393648
203179
136662
82531
372651
195898
132537
80408
Compensation with strategic culling
a= $5000
395359
a= $10000
200911
a= $15 000
134659
a=$25000
81140
a
Optimal elephant stocks (discount rate of 12% throughout).
E. Bulle, G. Corne lis van Kooten/ Agricultural Economics 27 (2002) 15-22
Note that elephant populations benefit from a trade
ban when r = 12% (the in situ stocks are somewhat
greater than the stocks reported in the third column of
Table 2), but also note that the main result of this paper still holds that international transfers may or may
not promote conservation if range states collude and
if there are diminishing returns to conservation. This
finding appears to be quite robust, and is also apparent
from the other three scenarios. Increasing total WTP
for conservation A and benefits from wildlife tourism
R(x) (agricultural damage D(x)) will support thicker
(smaller) elephant stocks, but the effect of providing
transfers is ambiguous depending on the steepness of
the "demand for nature" curve.
Optimal elephant stocks appear to be quite sensitive
to the specification of benefits and costs; the recommended stock size may be anywhere between as few
as 80 000 elephants and as many as the undisturbed,
carrying capacity population of 690 000 animals. This
strongly suggests that additional research should be
devoted towards estimating the relevant parameters before sensible management policies can be formulated.
5. Concluding remarks and discussion
Non-use values spill over national boundaries creating positive (or negative) externalities. When such
values are not compensated in the international arena,
sub-optimally low levels of wildlife amenities may result. However, the conventional remedy to overcome
this problem may provoke strategic responses by host
countries, resulting in loss of global welfare and excessive depletion of valuable resources. Hence, an international program to compensate range states where
wildlife are found needs to be carefully constructed.
Natural resource economists should progress beyond
CVM methods to strategic behavior mechanism analysis to come to grips with these problems.
The strategic behavior modeled in this paper resembles a problem known from the literature on
optimal pollution taxes (see Baumol and Oates, 1988,
pp. 86-89). Should compensation be paid to range
states based on the (globally) optimal population of
elephants or on the actual population in existence
at any point in time, as advocated by Skonhoft and
Solstad (1998)? Analogous to optimal pollution taxes,
if compensation is paid according to the stock of
21
elephants in existence at any given time, a cartel of
range states will take into account the effect of their
harvest decisions on the compensation to be paid.
Alternatively, the developed countries could simply
pay the compensation amount per elephant associated with what they consider to be the optimal in situ
stock, come what may. While varying compensation
(pollution taxes) iteratively over time will result in
convergence to the global optimal stock if range states
(polluters) act non-strategically, the invariant payment
(tax) is preferred when strategic behavior is possible
(a cartel or single polluter exists).
There are several reasons why implementing the
time invariant payment to international nature conservation is difficult in practice. First, the case of
sovereign nations is different from that of a national
authority that can impose taxes on (unwilling) firms.
Sovereign nations can turn the management problem
into a game where the compensation scheme is subject
to negotiation. The range states may threaten to cull
elephants below the non-cooperative equilibrium, unless compensation according to the iterative approach
is forthcoming. (Because this is not a credible threat,
the range states should be able to commit themselves
to this policy otherwise it would not work.) Second,
actual decision making in the arena of international nature conservation appears to be based on a piecemeal
approach. For example, the ivory trade ban (moratorium on commercial whaling or trade restrictions on
tropical timber) appears to be motivated by short-term
concerns and, possibly, pressure by certain interest
groups (see Hutton, 2000). The long-run optimum is
often not in view, highlighting the relevance of the
main lesson of this paper. Our numerical results indicate that failing to grasp this can have detrimental
consequences for conservation of elephants in Africa.
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